The set of real values of x satisfying the equation
${| x - 1 |}^{l o g_{3} (x^{2}) - 2 l o g_{x} (9)} = (x - 1)^{7}$
is

{2}

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{27, 81}

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{81}

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{2, 81}

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Solution

The correct option is C
{81}

${| x - 1 |}^{l o g_{3} (x^{2}) - 2 l o g_{x} (9)} = (x - 1)^{7} (l o g_{3} x^{2} - 2 l o g_{x} 9) l o g_{| x - 1 |} | x - 1 | = 7 l o g_{| x - 1 |} (x - 1) l o g_{3} x^{2} - 2 l o g_{x} 9 = 7 2 l o g_{3} x - 4 \times \frac{1}{l o g_{3} x} = 7 L e t l o g_{3} x = t 2 t - \frac{4}{t} = 7 2 t^{2} - 7 t - 4 = 0 (t - 4) (2 t + 1) = 0 t = 4, t = \frac{- 1}{2} l o g_{3} x = 4 l o g_{3} x = \frac{- 1}{2} x = 81, x = \frac{1}{\sqrt{3}} < 1 ∴ x \neq \frac{1}{\sqrt{3}}$

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